A Study of Curvature Tensors By Using Berwald's and Cartan'sHigher-Order Derivatives in Finsler Spaces
الكلمات المفتاحية:
Covariant Derivative of second orders، Weyl Tensor 〖 W〗_jkh^i، Cartan’s 3th ، Curvature Tensor〖 R〗_jkh^i and Cartan’s 4th Curvature Tensor〖 K〗_jkh^iالملخص
This research investigates the decomposition of curvature tensors in Finsler spaces using higher-order derivatives of Berwald and Cartan connections. By employing these derivatives, we aim to provide a more comprehensive understanding of the geometric structure of Finsler spaces. Previous studies have explored various types of recurrences and their implications for curvature tensors. However, a systematic analysis of decomposition using higher-order derivatives has been lacking. This paper fills this gap by introducing a new approach to decompose curvature tensors and analyzing the properties of the resulting components. Our findings contribute to the existing body of knowledge on Finsler geometry and may have potential applications in related fields. In this paper, we investigate some identities between Weyl’s curvature tensor and Cartan’s 3th Curvature Tensor . We first introduce the basic concepts of Weyl’s tensor and Cartan’s 3th Curvature Tensor . Then, we derive some identities between these two tensors. Finally, we apply these identities to some examples
